Open Access
Research
Systematic literature review and network meta-analysis in highly active relapsing–remitting multiple sclerosis and rapidly evolving severe multiple sclerosis Eline Huisman,1 Katerina Papadimitropoulou,1 James Jarrett,2 Matthew Bending,2 Zoe Firth,2 Felicity Allen,3 Nick Adlard3
To cite: Huisman E, Papadimitropoulou K, Jarrett J, et al. Systematic literature review and network meta-analysis in highly active relapsing–remitting multiple sclerosis and rapidly evolving severe multiple sclerosis. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016013430 ▸ Prepublication history and additional material is available. To view please visit the journal (http://dx.doi.org/ 10.1136/bmjopen-2016013430).
Received 11 July 2016 Revised 8 November 2016 Accepted 12 December 2016
1
Mapi Group, Houten, The Netherlands 2 Mapi Group, London, UK 3 Novartis Pharmaceuticals, Frimley, UK Correspondence to Nick Adlard; [email protected]
ABSTRACT Objective: Multiple sclerosis (MS) is a chronic, neurodegenerative autoimmune disorder affecting the central nervous system. Relapsing–remitting MS (RRMS) is the most common clinical form of MS and affects ∼85% of cases at onset. Highly active (HA) and rapidly evolving severe (RES) RRMS are 2 forms of RRMS amenable to disease-modifying therapies (DMT). This study explored the efficacy of fingolimod relative to other DMTs for the treatment of HA and RES RRMS. Methods: A systematic literature review (SLR) was conducted to identify published randomised controlled trials in HA and RES RRMS. Identified evidence was vetted, and a Bayesian network meta-analysis (NMA) was performed to evaluate the relative efficacy of fingolimod versus dimethyl fumarate (DMF) in HA RRMS and versus natalizumab in RES RRMS. Results: For HA RRMS, the SLR identified 2 studies with relevant patient subgroup data: 1 comparing fingolimod with placebo and the other comparing DMF with placebo. 3 studies were found for RES RRMS: 1 comparing fingolimod with placebo and 2 studies comparing natalizumab with placebo. NMA results in the HA population showed a favourable numerical trend of fingolimod versus DMF assessed for annualised relapse rate (ARR) and 3-month confirmed disability progression. For the RES population, the results identified an increase of ARR and 3-month confirmed disability progression for fingolimod versus natalizumab (not statistically significant). Sparse study data and the consequently high uncertainty around the estimates restricted our ability to demonstrate statistical significance in the studied subgroups. Conclusions: Data limitations are apparent when conducting an informative indirect comparison for the HA and RES RRMS subgroups as the subgroups analyses were retrospective analyses of studies powered to indicate differences across entire study populations. Comparisons across treatments in HA or RES RRMS will be associated with high levels of uncertainty until new data are collected for these subgroups.
Strengths and limitations of this study ▪ Comprehensive and robust search strategy developed to identify all relevant interventions for the treatment of relapsing–remitting MS (RRMS). ▪ Potential bias in the analyses since the baseline characteristics of the highly active (HA) and rapidly evolving severe (RES) subgroups could not be adequately evaluated in some studies. ▪ Accordingly, studies were only synthesised if the patient populations used the same definitions for HA and RES RRMS, which limited the impact of potential imbalances on network meta-analysis results. ▪ The limited evidence base prohibited adjustments for potential treatment effect modifiers.
INTRODUCTION Multiple sclerosis (MS) is a disease of the central nervous system where myelin within the brain or spinal cord becomes inflamed and is then destroyed by the immune system.1 It can be classified into three subtypes: relapsing and remitting MS (RRMS), secondary progressive MS and primary progressive MS. RRMS is the most common clinical form of MS and accounts for ∼85% of cases at onset.2 In RRMS, people have distinct attacks of symptoms which then fade away either partially or completely. Symptoms may not all be experienced at the same time but can include visual disturbance, lack of balance and dizziness, chronic fatigue, bladder problems, pain, muscle weakness or spasticity and cognitive impairment.3 Although there is still no cure for MS, research has shown major improvements in MS treatment over the past 20 years and multiple disease modifying therapies (DMT) have become available since then, including
Huisman E, et al. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016-013430
1
Open Access interferon-β, glatiramer acetate, teriflunomide, dimethyl fumarate (DMF), natalizumab, fingolimod and alemtuzumab.1 4 Many of these treatments focus on early phases of the disease, while fewer treatment options are available for patients with highly active (HA) or rapidly evolving severe (RES) RRMS. Data on populations of patients with HA and RES RRMS are the subject of the analysis. At the time of this study, HA RRMS was defined in the fingolimod label as an unchanged or increased relapse rate or ongoing severe relapses compared with the previous year despite treatment with at least one DMT,5 and RES RRMS is defined as two or more disabling relapses in the past year, and one or more gadolinium-enhancing lesions on MRI or increase in the T2 lesion load compared with previous MRI.5 With the availability of different disease-modifying therapies, there is a need to understand the relative efficacy of the available treatments in patients with HA or RES RRMS. Definitions of these RRMS subpopulations were not derived from Phase III trials but from post hoc subgroup analyses of licensing studies. A number of systematic literature reviews (SLRs) and network meta-analyses (NMAs) have been published over recent years in RRMS;6–8 however, none of them specifically focused on the relative efficacy of treatment options in patients with HA or RES RRMS. There are no published studies with head-to-head comparisons between all licensed disease-modifying therapies in HA and RES RRMS. It is therefore important to assess whether it is possible to use data from existing published studies to draw meaningful comparisons between the efficacy of DMTs in the HA and RES populations, particularly from the perspective of Health Technology Appraisal (HTA) decision-making. The objectives of this study were to conduct a SLR and to assess the feasibility of conducting a Bayesian NMA to evaluate the relative efficacy and safety of DMTs in patients with HA or RES RRMS.
METHODS Data sources A SLR following Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guidelines was performed using a prespecified protocol.9 A previous SLR was conducted in 2010 and this review was an update of that previous work, focusing on studies post-2010 (data on file). A predefined search strategy was devised using a combination of medical subject headings (MeSH), Emtree terms (in EMBASE) and freetext terms for prespecified interventions in RRMS (see online supplementary tables S1–S3). Searches were conducted in MEDLINE, EMBASE and the Cochrane Library on 14 November 2014 with no limits on language. Proceedings of scientific meetings (American Academy of Neurology, European Committee for Treatment and Research in Multiple Sclerosis) were searched for 2013 and 2014. In addition, the European 2
Medicines Agency, US Food and Drug Administration and the ClinicalTrials.gov register were also searched. Selection of studies The records title and abstract were screened by two independent reviewers following specific Population, Intervention(s), Comparator(s), Outcome(s) & Study Design (PICOS) study eligibility criteria (see online supplementary table S4). A third independent reviewer provided consensus when there was disagreement on the inclusion of the title/abstract of the record. In the cases where exclusion based on the titles/abstracts was not possible, the full text was retrieved and evaluated. The screening process was repeated for included full texts using the PICOS criteria for final study inclusion. Reasons for exclusion were noted in the screening file. The review was designed to capture randomised controlled trials (RCTs) in RRMS, regardless of disease activity, but studies not reporting in HA or RES RRMS were excluded during screening for the purpose of this NMA. Only treatments recommended for reimbursement in the UK for RRMS were of interest in the SLR, with a focus on the HA and RES subgroups. As a result, natalizumab was not deemed to be a comparator of interest in the HA RRMS population because it is not reimbursed for use in this indication within the National Health Service (NHS) in England.10 It should be noted that no restrictions were placed on the trial location of the included studies. Inclusion of studies in the NMA required the study to include an arm that could form a connection to one or more other studies in the network. Data extraction and critical appraisal Data extraction of studies included was performed by one reviewer and checked by a second reviewer. Information on study design, selection criteria, study population/patient characteristics and interventions was extracted into a data extraction form, followed by individual study treatment effects and associated uncertainty measures for the outcomes of interest. The methodological quality of the included studies was assessed with the National Institute for Health and Care Excellence (NICE) critical assessment checklist,11 as adapted from the Centres for Reviews and Dissemination (CRD) checklist for RCTs.12 The risk of bias in each individual study was evaluated based on the following items: adequate method of randomisation, adequate allocation concealment, similarity of groups, blinding, no unexpected imbalances in drop-out, no selective reporting and appropriate use of the intention-to-treat principle. The results of the critical appraisal of included studies are presented in online supplementary table S5. NMA feasibility assessment The feasibility assessment was performed in three steps: (1) the possibility of constructing a network of interlinked studies, (2) study design and patient characteristics that could modify the relative treatment effect were Huisman E, et al. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016-013430
Open Access investigated, and (3) data availability per outcome of interest was assessed. The efficacy outcomes of interest were annualised relapse rate (ARR) at 12 and 24 months, ARR at any reported time point, difference in change from baseline EDSS score at 12 or 24 months, difference in change from baseline EDSS score at any time point, and HR of 3-month and 6-month confirmed disability progression. Disability progression was selected as one of the key outcomes in this study because it has driven the health economic modelling of RRMS since the first health economic model developed in 2003 by the School of Health and Related Research (ScHARR).13 To reduce the risk of bias in an NMA, only data from studies with similar study design and patient populations should be compared. Although some variation in study or patient characteristics across studies can be expected, an NMA is only valid when no imbalances exist across comparisons in the study of patient characteristics that can act as effect modifiers.14 To assess the feasibility of a valid NMA, the network of interlinked RCTs was analysed for differences in study design, patient characteristics and outcome definitions that could potentially bias the relative treatment effects. The similarity of studies in the HA and RES RRMS populations was assessed, by evaluating the study design, patient population and outcome definitions of studies identified in the SLR.15 Statistical analysis The relative efficacy of the identified interventions for the treatment of HA or RES RRMS for the selected outcomes was evaluated using a Bayesian NMA. In a Bayesian analysis, credible intervals (CrIs) are used instead of CIs. CrIs assume that the true value of the point estimate is within 95% of the range, whereas CIs assume that if the analysis was replicated 100 times, 95% of the CIs would include the true value of the parameter. Trial results were reported as trial-based summary measures, that is, 3-month and 6-month confirmed disability progression at 24 months was reported as HRs and ARR at 24 months were reported as risk ratios. In these cases, we assumed a normal distribution for the continuous measure of the treatment effect. The modelling is performed in the log scale. The outputs of the analyses are summary measures, that is, HRs and risk ratios of the treatment of interest versus the comparator. A value equal to 1 translates to no difference between the competing treatments and a value lower than 1 translates to greater efficacy (lower hazard and/or a lower risk of relapse). Non-informative prior distributions were assumed for both outcomes. In the presence of non-informative priors, CrIs can be interpreted similarly to CIs using a frequentist approach. In addition, if the 95% CrIs do not include 1, results can be considered statistically significant when using non-informative priors. Prior distributions of the relative treatment effects were assumed to Huisman E, et al. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016-013430
be normal, with 0 mean and a variance of 10 000, while a uniform distribution with support from 0 to 5 was used as prior of the between-study SD. For each of the outcomes, fixed-effects and random-effects models were evaluated and the better fitting model was selected based on the deviance information criterion which adds a penalty term, equal to the number of effective parameters. The fixed-effects model assumes that there is no variation in the relative treatment effects across studies for a particular pairwise comparison. The observed differences for a particular comparison among study results are solely due to chance. The general fixed-effects model for NMA can be specified as follows: ( hjk ¼
mjb ;
b ¼ A,B,C if k ¼ b
mjb þ dbk ¼ mjb þ dAk –dAb ; k ¼ B,C,D if k is 0 after 0 b
dAA ¼0 where μjb is the outcome for treatment b in study j, and dbk is the fixed effect of treatment k relative to treatment b. The random-effects model assumes that the true relative effects are exchangeable across studies and can be described as a sample from a normal/Gaussian distribution whose mean is the pooled relative effect and SD reflects the heterogeneity. The model notation of the random-effects model is as follows: ( hjk ¼
mjb ;
b=A; B; C
mjb þ djbk ; k=B,C,D
if k=b if k is 0 after 0 b
djbk Nðdbk ; s2 Þ ¼ NðdAk dAb ; s2 Þ dAA ¼0 where δjbk are the trial-specific effects of treatment k relative to treatment b. These trial-specific effects are drawn from a random-effects distribution with the following properties: d jbk N ðdbk ; s2 Þ.16 Given the small number of studies included in the analyses (one publication per direct comparison), the fixed-effects model was chosen over the random-effects model. The posterior densities for unknown parameters were estimated using Markov chain Monte Carlo (MCMC) simulations. The results presented here were based on 80 000 iterations on two chains, with a burn-in of 20 000 iterations. Convergence was assessed by visual inspection of trace plots. The accuracy of the posterior estimates was assessed using the Monte Carlo error for each parameter (Monte Carlo error
Research
Systematic literature review and network meta-analysis in highly active relapsing–remitting multiple sclerosis and rapidly evolving severe multiple sclerosis Eline Huisman,1 Katerina Papadimitropoulou,1 James Jarrett,2 Matthew Bending,2 Zoe Firth,2 Felicity Allen,3 Nick Adlard3
To cite: Huisman E, Papadimitropoulou K, Jarrett J, et al. Systematic literature review and network meta-analysis in highly active relapsing–remitting multiple sclerosis and rapidly evolving severe multiple sclerosis. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016013430 ▸ Prepublication history and additional material is available. To view please visit the journal (http://dx.doi.org/ 10.1136/bmjopen-2016013430).
Received 11 July 2016 Revised 8 November 2016 Accepted 12 December 2016
1
Mapi Group, Houten, The Netherlands 2 Mapi Group, London, UK 3 Novartis Pharmaceuticals, Frimley, UK Correspondence to Nick Adlard; [email protected]
ABSTRACT Objective: Multiple sclerosis (MS) is a chronic, neurodegenerative autoimmune disorder affecting the central nervous system. Relapsing–remitting MS (RRMS) is the most common clinical form of MS and affects ∼85% of cases at onset. Highly active (HA) and rapidly evolving severe (RES) RRMS are 2 forms of RRMS amenable to disease-modifying therapies (DMT). This study explored the efficacy of fingolimod relative to other DMTs for the treatment of HA and RES RRMS. Methods: A systematic literature review (SLR) was conducted to identify published randomised controlled trials in HA and RES RRMS. Identified evidence was vetted, and a Bayesian network meta-analysis (NMA) was performed to evaluate the relative efficacy of fingolimod versus dimethyl fumarate (DMF) in HA RRMS and versus natalizumab in RES RRMS. Results: For HA RRMS, the SLR identified 2 studies with relevant patient subgroup data: 1 comparing fingolimod with placebo and the other comparing DMF with placebo. 3 studies were found for RES RRMS: 1 comparing fingolimod with placebo and 2 studies comparing natalizumab with placebo. NMA results in the HA population showed a favourable numerical trend of fingolimod versus DMF assessed for annualised relapse rate (ARR) and 3-month confirmed disability progression. For the RES population, the results identified an increase of ARR and 3-month confirmed disability progression for fingolimod versus natalizumab (not statistically significant). Sparse study data and the consequently high uncertainty around the estimates restricted our ability to demonstrate statistical significance in the studied subgroups. Conclusions: Data limitations are apparent when conducting an informative indirect comparison for the HA and RES RRMS subgroups as the subgroups analyses were retrospective analyses of studies powered to indicate differences across entire study populations. Comparisons across treatments in HA or RES RRMS will be associated with high levels of uncertainty until new data are collected for these subgroups.
Strengths and limitations of this study ▪ Comprehensive and robust search strategy developed to identify all relevant interventions for the treatment of relapsing–remitting MS (RRMS). ▪ Potential bias in the analyses since the baseline characteristics of the highly active (HA) and rapidly evolving severe (RES) subgroups could not be adequately evaluated in some studies. ▪ Accordingly, studies were only synthesised if the patient populations used the same definitions for HA and RES RRMS, which limited the impact of potential imbalances on network meta-analysis results. ▪ The limited evidence base prohibited adjustments for potential treatment effect modifiers.
INTRODUCTION Multiple sclerosis (MS) is a disease of the central nervous system where myelin within the brain or spinal cord becomes inflamed and is then destroyed by the immune system.1 It can be classified into three subtypes: relapsing and remitting MS (RRMS), secondary progressive MS and primary progressive MS. RRMS is the most common clinical form of MS and accounts for ∼85% of cases at onset.2 In RRMS, people have distinct attacks of symptoms which then fade away either partially or completely. Symptoms may not all be experienced at the same time but can include visual disturbance, lack of balance and dizziness, chronic fatigue, bladder problems, pain, muscle weakness or spasticity and cognitive impairment.3 Although there is still no cure for MS, research has shown major improvements in MS treatment over the past 20 years and multiple disease modifying therapies (DMT) have become available since then, including
Huisman E, et al. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016-013430
1
Open Access interferon-β, glatiramer acetate, teriflunomide, dimethyl fumarate (DMF), natalizumab, fingolimod and alemtuzumab.1 4 Many of these treatments focus on early phases of the disease, while fewer treatment options are available for patients with highly active (HA) or rapidly evolving severe (RES) RRMS. Data on populations of patients with HA and RES RRMS are the subject of the analysis. At the time of this study, HA RRMS was defined in the fingolimod label as an unchanged or increased relapse rate or ongoing severe relapses compared with the previous year despite treatment with at least one DMT,5 and RES RRMS is defined as two or more disabling relapses in the past year, and one or more gadolinium-enhancing lesions on MRI or increase in the T2 lesion load compared with previous MRI.5 With the availability of different disease-modifying therapies, there is a need to understand the relative efficacy of the available treatments in patients with HA or RES RRMS. Definitions of these RRMS subpopulations were not derived from Phase III trials but from post hoc subgroup analyses of licensing studies. A number of systematic literature reviews (SLRs) and network meta-analyses (NMAs) have been published over recent years in RRMS;6–8 however, none of them specifically focused on the relative efficacy of treatment options in patients with HA or RES RRMS. There are no published studies with head-to-head comparisons between all licensed disease-modifying therapies in HA and RES RRMS. It is therefore important to assess whether it is possible to use data from existing published studies to draw meaningful comparisons between the efficacy of DMTs in the HA and RES populations, particularly from the perspective of Health Technology Appraisal (HTA) decision-making. The objectives of this study were to conduct a SLR and to assess the feasibility of conducting a Bayesian NMA to evaluate the relative efficacy and safety of DMTs in patients with HA or RES RRMS.
METHODS Data sources A SLR following Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guidelines was performed using a prespecified protocol.9 A previous SLR was conducted in 2010 and this review was an update of that previous work, focusing on studies post-2010 (data on file). A predefined search strategy was devised using a combination of medical subject headings (MeSH), Emtree terms (in EMBASE) and freetext terms for prespecified interventions in RRMS (see online supplementary tables S1–S3). Searches were conducted in MEDLINE, EMBASE and the Cochrane Library on 14 November 2014 with no limits on language. Proceedings of scientific meetings (American Academy of Neurology, European Committee for Treatment and Research in Multiple Sclerosis) were searched for 2013 and 2014. In addition, the European 2
Medicines Agency, US Food and Drug Administration and the ClinicalTrials.gov register were also searched. Selection of studies The records title and abstract were screened by two independent reviewers following specific Population, Intervention(s), Comparator(s), Outcome(s) & Study Design (PICOS) study eligibility criteria (see online supplementary table S4). A third independent reviewer provided consensus when there was disagreement on the inclusion of the title/abstract of the record. In the cases where exclusion based on the titles/abstracts was not possible, the full text was retrieved and evaluated. The screening process was repeated for included full texts using the PICOS criteria for final study inclusion. Reasons for exclusion were noted in the screening file. The review was designed to capture randomised controlled trials (RCTs) in RRMS, regardless of disease activity, but studies not reporting in HA or RES RRMS were excluded during screening for the purpose of this NMA. Only treatments recommended for reimbursement in the UK for RRMS were of interest in the SLR, with a focus on the HA and RES subgroups. As a result, natalizumab was not deemed to be a comparator of interest in the HA RRMS population because it is not reimbursed for use in this indication within the National Health Service (NHS) in England.10 It should be noted that no restrictions were placed on the trial location of the included studies. Inclusion of studies in the NMA required the study to include an arm that could form a connection to one or more other studies in the network. Data extraction and critical appraisal Data extraction of studies included was performed by one reviewer and checked by a second reviewer. Information on study design, selection criteria, study population/patient characteristics and interventions was extracted into a data extraction form, followed by individual study treatment effects and associated uncertainty measures for the outcomes of interest. The methodological quality of the included studies was assessed with the National Institute for Health and Care Excellence (NICE) critical assessment checklist,11 as adapted from the Centres for Reviews and Dissemination (CRD) checklist for RCTs.12 The risk of bias in each individual study was evaluated based on the following items: adequate method of randomisation, adequate allocation concealment, similarity of groups, blinding, no unexpected imbalances in drop-out, no selective reporting and appropriate use of the intention-to-treat principle. The results of the critical appraisal of included studies are presented in online supplementary table S5. NMA feasibility assessment The feasibility assessment was performed in three steps: (1) the possibility of constructing a network of interlinked studies, (2) study design and patient characteristics that could modify the relative treatment effect were Huisman E, et al. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016-013430
Open Access investigated, and (3) data availability per outcome of interest was assessed. The efficacy outcomes of interest were annualised relapse rate (ARR) at 12 and 24 months, ARR at any reported time point, difference in change from baseline EDSS score at 12 or 24 months, difference in change from baseline EDSS score at any time point, and HR of 3-month and 6-month confirmed disability progression. Disability progression was selected as one of the key outcomes in this study because it has driven the health economic modelling of RRMS since the first health economic model developed in 2003 by the School of Health and Related Research (ScHARR).13 To reduce the risk of bias in an NMA, only data from studies with similar study design and patient populations should be compared. Although some variation in study or patient characteristics across studies can be expected, an NMA is only valid when no imbalances exist across comparisons in the study of patient characteristics that can act as effect modifiers.14 To assess the feasibility of a valid NMA, the network of interlinked RCTs was analysed for differences in study design, patient characteristics and outcome definitions that could potentially bias the relative treatment effects. The similarity of studies in the HA and RES RRMS populations was assessed, by evaluating the study design, patient population and outcome definitions of studies identified in the SLR.15 Statistical analysis The relative efficacy of the identified interventions for the treatment of HA or RES RRMS for the selected outcomes was evaluated using a Bayesian NMA. In a Bayesian analysis, credible intervals (CrIs) are used instead of CIs. CrIs assume that the true value of the point estimate is within 95% of the range, whereas CIs assume that if the analysis was replicated 100 times, 95% of the CIs would include the true value of the parameter. Trial results were reported as trial-based summary measures, that is, 3-month and 6-month confirmed disability progression at 24 months was reported as HRs and ARR at 24 months were reported as risk ratios. In these cases, we assumed a normal distribution for the continuous measure of the treatment effect. The modelling is performed in the log scale. The outputs of the analyses are summary measures, that is, HRs and risk ratios of the treatment of interest versus the comparator. A value equal to 1 translates to no difference between the competing treatments and a value lower than 1 translates to greater efficacy (lower hazard and/or a lower risk of relapse). Non-informative prior distributions were assumed for both outcomes. In the presence of non-informative priors, CrIs can be interpreted similarly to CIs using a frequentist approach. In addition, if the 95% CrIs do not include 1, results can be considered statistically significant when using non-informative priors. Prior distributions of the relative treatment effects were assumed to Huisman E, et al. BMJ Open 2017;7:e013430. doi:10.1136/bmjopen-2016-013430
be normal, with 0 mean and a variance of 10 000, while a uniform distribution with support from 0 to 5 was used as prior of the between-study SD. For each of the outcomes, fixed-effects and random-effects models were evaluated and the better fitting model was selected based on the deviance information criterion which adds a penalty term, equal to the number of effective parameters. The fixed-effects model assumes that there is no variation in the relative treatment effects across studies for a particular pairwise comparison. The observed differences for a particular comparison among study results are solely due to chance. The general fixed-effects model for NMA can be specified as follows: ( hjk ¼
mjb ;
b ¼ A,B,C if k ¼ b
mjb þ dbk ¼ mjb þ dAk –dAb ; k ¼ B,C,D if k is 0 after 0 b
dAA ¼0 where μjb is the outcome for treatment b in study j, and dbk is the fixed effect of treatment k relative to treatment b. The random-effects model assumes that the true relative effects are exchangeable across studies and can be described as a sample from a normal/Gaussian distribution whose mean is the pooled relative effect and SD reflects the heterogeneity. The model notation of the random-effects model is as follows: ( hjk ¼
mjb ;
b=A; B; C
mjb þ djbk ; k=B,C,D
if k=b if k is 0 after 0 b
djbk Nðdbk ; s2 Þ ¼ NðdAk dAb ; s2 Þ dAA ¼0 where δjbk are the trial-specific effects of treatment k relative to treatment b. These trial-specific effects are drawn from a random-effects distribution with the following properties: d jbk N ðdbk ; s2 Þ.16 Given the small number of studies included in the analyses (one publication per direct comparison), the fixed-effects model was chosen over the random-effects model. The posterior densities for unknown parameters were estimated using Markov chain Monte Carlo (MCMC) simulations. The results presented here were based on 80 000 iterations on two chains, with a burn-in of 20 000 iterations. Convergence was assessed by visual inspection of trace plots. The accuracy of the posterior estimates was assessed using the Monte Carlo error for each parameter (Monte Carlo error
